Question

Solve using elimination.

x+y=11
x−8y=−25

Answer 1

x = 7

y = 4

Explanation:

The elimination method is a way to solve a system of linear equations by adding or subtracting the equations in a way that eliminates one of the variables.

In order to solve the system of equations using elimination, we can do the following:

Rearrange the equations so that the coefficients of one of the variables are negative inverses of each other.

In this case, we can rearrange the first equation as follows:

`\sf x + y = 11 ......[I]`

And the second equation as follows:

`\sf x + 8y = -25 ......[ii]`

Add the equations together.

Than we subtract the equations [i] by equation [ii].

`\sf x + y - (x-8y) = 11-(-25)`

Opening bracket

`\sf x + y - x+8y = 11+25`

Simplify like terms:

`\sf 9y = 36`

Dividing both sides of the equation by 9, we get:

`\sf y = (36)/(9)`

`\sf y = 4`

Now,

To solve for x.

Multiply equation 1 by 8 to make the coefficients of x in both equations equal:

`\sf 8(x + y) = 8(11)`

`\sf 8x + 8y = 88.......[iii]`

Now, add the equation [ii] to the equation [iii] to eliminate the y variable:

`\sf (8x + 8y) + (x - 8y) = 88 - 25`

Combine like terms:

`\sf 9x = 63`

Divide both sides by 9 to solve for x:

`\sf (9x)/(9 )= (63)/(9)`

x = 7

Therefore, x = 7 and y = 4.